3.6 Types of Triangles

1. 3.6 Types of Triangles • Objectives: • Name the various types of triangles and their parts • Use different types of triangles in proofs

2. B B vertex angle A A C C base angles scalene triangle: a triangle with no two sides congruent. isosceles triangles: a triangle with at least two sides congruent. Proof reasons: If , then The converse of this is true as well!!!! legs legs base

3. B A C B A C equilateral triangle: a triangle with all sides congruent. equiangular triangle: a triangle with all angles congruent.

4. B B A A C C acute triangle: a triangle with all acute angles. right triangle:a triangle with a right angle. hypotenuse leg leg

5. B A C obtuse triangle: a triangle with an obtuse angle.

6. Naming triangles: Example 1: a) 40° 70° 70° ______________ _____________ triangle angle name side name

7. b) ______________ _____________ triangle angle name side name

8. c) ______________ _____________ triangle angle name side name 70° 60° 50°

9. d) ______________ _____________ triangle angle name side name

10. e) ______________ _____________ triangle angle name side name 120° 30° 30°

11. f) ______________ _____________ triangle angle name side name

12. Example 2: Scalene, Isosceles, or Equilateral? Perimeter = 94 units 8x +10 7x – 2 x2 +10 Isosceles

13. Example 2: A C B D E AED CDE Given Given BED BDE Reflexive Property ASA ∆ADE ∆CED CPCTC Given Subtraction Property ∆EBD is isosceles Definition of isosceles

14. Example 3: Q R U T S Given Given Given Definition of perpendicular lines QTS and RST are right angles All right angles are congruent QTSRST Reflexive Property ∆QTS ∆RST SAS CPCTC Continued on next slide

15. Example 3: Q R U T S Given Definition of isosceles Subtraction Property Definition of isosceles

16. A Example 4: F B E C D Given Definition of equilateral Definition of equiangular AEF is supp. to AED Linear Pair Postulate ACB is supp. to ACD Linear Pair Postulate AEF  ACB Congruent Supplements Thm. Definition of equilateral Given Continued on next slide

17. A Example 4: F B E C D SAS ∆AEF  ∆ACB CPCTC Definition of isosceles